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<h1>paley
</h1>

<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2>
<div class="box"><strong>paley(g,n) --- create a Paley graph with n vertices</strong></div>

<h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2>
<div class="box"><strong>function paley(g,n) </strong></div>

<h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2>
<div class="fragment"><pre class="comment"> paley(g,n) --- create a Paley graph with n vertices
 In this graph, there is an edge from i to j iff i-j is a square in Z_n.
 Hence, if -1 is not a square in Z_n, an error is generated.</pre></div>

<!-- crossreference -->
<h2><a name="_cross"></a>CROSS-REFERENCE INFORMATION <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2>
This function calls:
<ul style="list-style-image:url(../../matlabicon.gif)">
<li><a href="add.html" class="code" title="function add(g,i,j)">add</a>	add --- add edge(s) to the graph</li><li><a href="resize.html" class="code" title="function resize(g, n)">resize</a>	resize(g,n) --- change the number of vertices in g to n</li><li><a href="rmxy.html" class="code" title="function rmxy(g)">rmxy</a>	rmxy(g) --- erase g's embedding</li></ul>
This function is called by:
<ul style="list-style-image:url(../../matlabicon.gif)">
</ul>
<!-- crossreference -->


<h2><a name="_source"></a>SOURCE CODE <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2>
<div class="fragment"><pre>0001 <a name="_sub0" href="#_subfunctions" class="code">function paley(g,n)</a>
0002 <span class="comment">% paley(g,n) --- create a Paley graph with n vertices</span>
0003 <span class="comment">% In this graph, there is an edge from i to j iff i-j is a square in Z_n.</span>
0004 <span class="comment">% Hence, if -1 is not a square in Z_n, an error is generated.</span>
0005 
0006 <span class="keyword">if</span> (n &lt;= 1) 
0007     error(<span class="string">'n must be at least 2'</span>);
0008 <span class="keyword">end</span>
0009 
0010 squares = unique(mod((1:n-1).^2,n));
0011 
0012 <span class="comment">% check if -1 is a square</span>
0013 <span class="keyword">if</span> ~ismember(n-1,squares)
0014     error(<span class="string">'-1 is not a square in Z_n'</span>);
0015 <span class="keyword">end</span>
0016 <a href="resize.html" class="code" title="function resize(g, n)">resize</a>(g,0);
0017 <a href="resize.html" class="code" title="function resize(g, n)">resize</a>(g,n);
0018 <a href="rmxy.html" class="code" title="function rmxy(g)">rmxy</a>(g);
0019 <span class="keyword">for</span> v = 1:n
0020     nlist = mod(v+squares,n);
0021     idx = find(nlist == 0);
0022     <span class="keyword">if</span> length(idx)&gt;0
0023         nlist(idx) = n;
0024     <span class="keyword">end</span>
0025     <span class="keyword">for</span> w = nlist
0026         <a href="add.html" class="code" title="function add(g,i,j)">add</a>(g,v,w)
0027     <span class="keyword">end</span>
0028 <span class="keyword">end</span></pre></div>
<hr><address>Generated on Fri 30-Apr-2010 07:51:16 by <strong><a href="http://www.artefact.tk/software/matlab/m2html/">m2html</a></strong> &copy; 2003</address>
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